In a circle, a central angle intercepts an arc of 75 degrees. If the area of the circle is 144π, what is the area of the sector formed by this central angle?
Correct: C
The area of the circle is given as A_circle = 144π.
The formula for the area of a sector (A_sector) is A_sector = (θ/360°) * A_circle, where θ is the central angle in degrees.
Given θ = 75 degrees and A_circle = 144π.
A_sector = (75/360) * 144π
Simplify the fraction 75/360. Both are divisible by 15: 75/15 = 5, 360/15 = 24. So, 75/360 = 5/24.
A_sector = (5/24) * 144π
Since 144 / 24 = 6:
A_sector = 5 * 6π
A_sector = 30π square units.